Can you please shed some light on healing by faith versus healing through physicians and medication from an Islamic point of view.

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
The legal Islamic Ruqyah (healing by Qur'an and Du'a) is done under three conditions:
1. It has to be by the names or characteristics of Allah.
2. It should be in the Arabic language and with words that can be understood. Any ambiguous or incomprehensible word should be avoided in the Ruqyah because it is disliked to make Du'a in any language other than Arabic. Ibn Taymiyyah mentioned this as another condition.
3. The one who does the Ruqyah and the one to whom it is done must believe that it cannot have any effect by itself. It is only by the will of Allah. If these three conditions are met the Ruqyah is legal. The Prophet said: "There is no harm in the Ruqyah as long as it is not Shirk (Polytheism).
On the other hand, there is no contradiction between being treated by experimental medicine or by the Ruqyah because the Islamic Ruqyah does not only treat the psychological and mental disease but also the physical diseases. The person is allowed to seek the treatment as long as it does not go beyond the Shariah limits.
As for the Islamic rule concerning seeking treatment in general, one should know that the sickness is predestination from Allah The Almighty. This in fact is only a kind of linking the cause and the causative. The Prophet answered Abu Khuzaymah when he asked him: "O! Prophet of Allah, how about a Ruqyah we use as amulets, some medicine we use as a treatment, … do these repulse some of what was predestined by Allah?" The Prophet said: "These are all from Allah's predestination". (Ahmed) Muslim also narrated from Jabir Ibn Abdullah that the Prophet said: "For each sickness (disease) there is a remedy, if the appropriate remedy is taken for the sickness it is cured by the will of Allah". Muslim and Bukhari narrated from Abu Hurayrah that he said: "Allah has not sent down any disease without sending its remedy".
It is also narrated in Al-Musnad that the Prophet said: "Yes, Oh servants of Allah, seek remedy as Allah has not made any disease without making a cure for it except one sickness: decrepitude. In another narration of the same Hadeeth he said: "Allah has not sent down any sickness without sending a remedy for it; still some will know it and some will ignore it".
These sacred narrations show that the person is asked to seek remedy but it is not obligatory on him to do so. This is the opinion of the majority of Muslim Scholars.
The Prophet's saying, "For each disease, there is a remedy", gives hope to all sick people as well as doctors and raise their spirits. Hence, when the sick person comes to know that there is a remedy for his disease, he becomes more courageous, more hopeful and more optimistic. And, when the doctor knows that there is a cure for a given disease, he starts to search and look for this remedy. This is yet another evidence of Muhammad's prophecy as he informed us that all diseases sent by Allah have cures except decrepitude. Having known this, one should also know that we are allowed to treated only by lawful means.
In fact, it is forbidden to be treated with anything forbidden (edible like: pork, drinkable like alcohol, audible like: Music). The Prophet said: "Allah has not made my Ummah's remedy in what He has forbidden to them" (Ahmad). So, whoever believes a remedy can be found in a forbidden thing has committed a sin, because the Ummah's remedy was not put in a forbidden thing.

Allah knows best.